Math 3150-4 Final review sheet
1.1-1.2 (preliminaries): What is a partial dierential equation? Is a dierential equation linear or non-linear? Homogeneous or non-homogeneous?
What is the order of a dierential equation?
2.1 (periodic functions) you should
Math 3150-4 Midterm 2 review sheet
3.4 (DAlemberts method) You should know the form of DAlemberts
solution to the 1D Wave Equation in the general case (both initial condition and initial velocity are given). You also should be able to verify
that solutio
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% Sample code f o r problem 3 . 7 . 2 :
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% Square membrane w i t h s i d e 1 , wave v e l o c i t y c=1/ p i and
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i n i t i a l shape
u ( x , y , 0 ) = f ( x , y ) = sin ( pi x ) sin ( pi y )
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initial velocity
u t (x , y ,0) = g (x
Math 3150-4, Practice Final
Spring 2012
Total points: 130/120.
Notes: Problems are independent of each other. This practice exam is longer and more
dicult than the actual exam.
Problem 1 (10 pts) Consider a bar of length L. The position on the bar is give
'Math 3150-4, Midterm Exam 2
I A , Spring 2012
Name: 30" 03 uNID:
Total points: 110/100 (subject to change). Total problems: 5.
Note: Problems are independent of each other.
Problem 1 (20 pts) Consider the heat equation on a bar of length 7r with inhom
MATH 3150-4, PRACTICE MIDTERM EXAM 2
SPRING 2012
Total points: 100/100.
Problem 1 (30 pts) The goal of this problem is to solve the Heat Equation with mixed
boundary conditions
ut = 3uxx for 0 < x < 1 and t > 0
ux (0, t) = 0
for t > 0
(1)
u(1, t) = 0
fo